Slope Grade & Ratio Calculator
Turn rise and run into slope ratio, percentage grade, and angle — for algebra homework, ramps, roofs, roads, and drainage. Free, instant, works on your phone.
Slope shows up in two very different contexts: a coordinate-geometry problem asking for "the slope between two points," and a real-world measurement — a ramp, a roof, a driveway — that needs to meet a specific standard. This calculator handles both, converting between ratio, percentage grade, angle, and decimal slope from a single rise and run.
Ratio, percentage, and angle are the same slope, three ways
A slope of 1:12 (rise:run), 8.33% grade, and 4.76° are all describing the exact same steepness — just in the format a specific field prefers. Construction and accessibility standards almost always use ratio or percentage. Algebra and trigonometry problems usually want the decimal slope (m) or the angle. Converting between them by hand means running the same rise/run numbers through three different formulas — this calculator does all three from one entry.
Why real-world slope has actual pass/fail thresholds
Unlike a homework problem, a ramp or roof slope isn't just a number — it's checked against a standard. A wheelchair ramp steeper than 1:12 (8.33%) fails ADA guidelines in the US. A roof pitched too shallow won't drain water properly. A road grade above roughly 8-10% starts to matter for vehicle handling and winter safety. The reference table above gives common thresholds as a starting point — always confirm the exact figure against your local building code, since requirements vary by jurisdiction and specific application.
Frequently asked questions
Do I need to use the same unit for rise and run?
Yes — as long as both measurements use the same unit (both in inches, or both in feet, for example), the calculated ratio and percentage will be correct. The specific unit doesn't matter for the result, only that rise and run match each other.
What slope is considered a wheelchair-accessible ramp?
US ADA guidelines set a maximum running slope of 1:12 (8.33%) for standard ramps, with 1:16 to 1:20 considered more comfortable for independent use. Always verify against current ADA standards or your local code for an actual installation, since requirements can be stricter for certain situations.
Why does my textbook use "m" for slope instead of degrees or percentage?
In algebra, slope (m) is defined as rise over run as a plain decimal or fraction — it's the coefficient in the line equation y = mx + b. Percentage and angle are more common in construction and everyday measurement, but they describe the identical steepness, just converted to a different format.
What roof pitch is normal for a house?
Most residential roofs fall somewhere between a 4:12 and 9:12 pitch (roughly 33% to 75% grade), with the right choice depending on climate, roofing material, and architectural style — steeper pitches shed snow and rain more effectively but cost more to build.
Why is my calculated angle so much smaller than the percentage grade suggests?
Percentage grade and angle relate through a tangent function, not a straight 1-to-1 scale — a 100% grade is a 45° angle, not 100°. At lower slopes especially, percentage grade grows noticeably faster than the angle does, which is why a "steep-sounding" 50% grade is actually just a 26.57° incline.